I’ve been making some diagrams, diagram-drawings. I realised whilst making these that they are all un-knots – so long as I carried on drawing my new line crossing beneath everything that was already there, i.e. being the broken line, they always would represent un-knots – disentangle completely to leave nothing but a loop. To make a knot that does anything more interesting, then, the drawer must at some point place their line over an earlier piece of line, which is what requires the odd process of either earlier on leaving a gap for a line to then cross over (often imperfectly), or erasing the line that’s already there. That requires a temporal disruption, a glitch in the sequence of the drawing, and neither of those gap-leaving devices works particularly comfortably.
The thing I’m abandoning here is the requirement for economy in a useful knot diagram. Relevance Theory – these include a lot of detail and swoops and crossings that really aren’t relevant, that provide all sorts of useless extra information that needs processing but offers a whole lot of no benefit. One of them I’ve even abandoned the smooth lines. Ouch.